There are a lot of variables that go into this that you haven't quite addresses.
First off, what is the point of teeth? We can answer that by looking at what teeth are used for today:
- Grasp and hold prey.
- Kill prey.
- Remove flesh from prey.
- Break down food to prevent choking.
- Break down food to aid in digestion.
Let's go with those five. Even there, teeth do not need to be hard and strong to perform their function: look at most fish, for an example. So we may have to re-evaluate that condition.
We also know that teeth must be able to resist whatever they regularly come in contact with. For example, if a creature's primary prey is a highly acidic monster, it will probably evolve teeth that resist such acid.
Second, assuming any arbitrary alien physiology, teeth will most likely be made of whatever their main structural support system is made of. We also see this on earth.
Realistically, teeth could be made of almost anything. On earth, we know of bacteria that eat iron, steel, etc. These processes could be reversed in the correct environment with energy input, and it's not inconceivable to imagine such a process evolving in an environment rich enough in the material.
Also, it doesn't have to be minerals. On the organic side of the spectrum, we see organic material used to make hard and strong sea-shells and squid beaks. It's highly possible that this material could be used to make teeth.
Really, teeth are more a function of the prey/food then they are the materials available. There's almost always some combination of materials in an environment that can make a teeth-like substance sufficient for consuming whatever prey/food is in our creature's ecological niche.